
where \(\bar{t} = 0.3\)  s is a constant prediction time. The future position \((x_{k+1},y_{k+1})\)  is computed by an arc approximation similar to [1]}. The radius \(r = \frac{v_k\,+\,0.5\,\bar{t}\,a}{w_k\,+\,0.5\,\bar{t}\,b}\)  of the arc is obtained from the linear and angular velocities in the middle of the prediction interval \(\bar{t}\) .
